Chemotherapy related anemia occurs in a majority of cancer patients and can cause impaired treatment outcomes, increased treatment-related complications and altered quality of life. Epoetin alfa administered on a weekly dosing schedule of 40,000 Units subcutaneously ([SC], under the skin) with dose adjustments based on hematologic response produces significant improvement in hemoglobin levels, decreased transfusion frequency and improved quality of life. It is unknown if the recently developed agent, darbepoetin alfa, administered on an every other week fixed dose will produce similar improvements in hematologic and quality of life outcomes. Thus, further randomization studies are warranted utilizing once weekly dosing (QW) of Epoetin alfa compared to once every other week (Q2W) darbepoetin alfa. Patients will receive study medications for up to 16 weeks.Safety & efficacy evaluations will be performed at specified intervals throughout the study.The study hypothesis is that the Week 5 hemoglobin response rate in the Epoetin alfa group is better than that in the Darbepoetin alfa group. The starting dose for study drug is either Epoetin alfa (PROCRIT) 40,000 Units SC QW or Darbepoetin alfa (ARANESP) 200 mcg SC Q2W. Doses may be adjusted depending on the patient's hemoglobin levels up a maximum of 60,000 IU SC QW Epoetin alfa or 300 mcg SC Q2W Darbepoetin alfa.